The following invention relates to basket options and, in particular, to a method for hedging risks associated with basket options.
Basket options are options whose return is based upon the average performance of a pre-set basket of underlying assets. The underlying assets contained in the basket may be of any security type including currencies, equities or commodities. Basket options are typically used to manage the risk associated with a number of securities with a single transaction.
For example, a call option on a basket of currencies gives a buyer of the option the right to receive the currencies designated in the basket in exchange for a base currency either at a prevailing Foreign Exchange (FX) rate or another prearranged rate of exchange. The strike price of the option is based on the weighted value of the component currencies, calculated in the buyer's base currency. In forming the basket option, the buyer may stipulate the maturity of the option, the foreign currency amounts which make up the basket, and the strike price which is expressed in units of the base currency. At option expiration, if the total value of the component currencies in the spot market is less than the strike price of the basket option, then the option expires worthless for calls. If, however, the total value of the component currencies is more than the strike price, the buyer would exercise the option and exchange all of the component currencies for the pre-specified amount of base currency (i.e. the strike price of the option).
While the pricing of an option on an individual security is typically determined using an options pricing model, such as the Black-Scholes model, the price of a basket option also depends on the correlation between the components in the basket. In particular, as the correlation between the basket components increases, the price of the basket option increases, while if the correlation between the basket components decreases, the price of the basket option decreases. The pricing of a basket option therefore includes a risk factor associated with the correlation between the components in the basket.
Institutions that trade basket options look to minimize the correlation risk associated with the basket options. One way to hedge the correlation risk is to enter into another transaction that depends on the same correlation factors included in the basket option. For example, if an institution buys a basket option on the stocks that are included in the S&P 500 then trading options on the Standard and Poor's Index would hedge the correlation risk associated with the basket option.
In many instances, however, a transaction for hedging the correlation risk associated with a particular basket option is unavailable. This is especially the case for basket options including foreign exchanges instruments because there are typically few, if any, FX baskets traded that can be used for hedging purposes. Without a hedging transaction to protect against the correlation risk associated with basket options, institutions either increase the premium for which they are willing to trade such basket options to cover the correlation risk or are deterred from trading basket options altogether.
Accordingly, it is desirable to provide a method for hedging the correlation risk associated with basket options.